Volume 50, Issue 12, 15 June 1969

Molecular Schrödinger Equation. IX. Square and Rectangular States of H_{4} and the Molecular Ions H_{4} ^{3+} and H_{4} ^{2+}
View Description Hide DescriptionOur method for the solution of the molecular Schrödinger equation has been further developed and extended to the case of the four‐electron system. Ab initio calculations are presented which lead to the electronic wavefunctions and energies of square and rectangular forms of H_{4}. As a preliminary to the four‐electron studies, the energies and wavefunctions for a number of states of the ions H_{4} ^{3+} and H_{4} ^{2+} are calculated. Complete contour maps for the potential energy surfaces of these systems are reported and the H_{4}surface is discussed in connection with the bimolecular isotopeexchange reaction H_{2}+D_{2}→2HD. Contour maps for the electron density distribution in square and rectangular H_{4} are presented and discussed.

Vapor Pressure and Crystal Structure of Curium Metal
View Description Hide DescriptionThe vapor pressure of liquid and solidcuriummetal between 1179° and 2068°K and between 10^{−10} atm and 0.1 mm was measured by the Knudsen effusion method to be and for vaporization are 82.6 ± 2.7 kcal/g·atm and 21.7 ± 1.7 eu, respectively. A previously unreported fcc close‐packed structure for curiummetal was identified with , and a density of 19.26 g/cm^{3}, corresponding to a +4 metallic valence. The entropy of condensed curium is indicated to be relatively high by the low heat of fusion and by the for vaporization calculated by second‐ and third‐law methods. The heat of vaporization of curium may be explained from the opposing effects of a quadrivalent metal and a to transition on vaporization.

ESR Study of the Kinetics of the Reaction of H Atoms with Methane
View Description Hide DescriptionA wide‐temperature‐range study using ESR atom detection has been employed to measure the rate of the reaction H + CH_{4}→H_{2} + CH_{3}. Over the temperature range 426°–747°K, we obtain a specific rate constant for the above reaction of expressed in units of cubic centimeters per mole per second. The value obtained in the present work is compared to a number of other results obtained by various workers. The activation energy we observe is considerably higher than previous values obtained in this temperature range. However, our results coupled with the heat of the reaction predict an activation energy for the reverse reaction which agrees well with experimental values. In addition, the pre‐exponential factor we obtain agrees with absolute rate theory predictions as well as with entropy considerations. We do not agree with literature results which give very low pre‐exponential factors suggesting steric factors of the order of 10^{−3}–10^{−5} for this reaction.

Molecular Freedom of the Ammonium Ion. Heat Capacity and Thermodynamic Properties of Ammonium Perchlorate from 5°–350°K
View Description Hide DescriptionThe heat capacity of NH_{4}ClO_{4} has been determined by adiabatic calorimetry from 5°–350°K and found to be of simple sigmate character without thermal anomalies. The heat capacity, entropy, enthalpy function , and Gibbs energy function evaluated at 298.15°K from these data are 30.61, 44.02, 20.24, and −23.78 cal/(gfm °K). Combination of these values with aqueous NH_{4}ClO_{4}thermochemical data suggests the absence of zero‐point entropy. Comparison with the heat capacity of isostructural KClO_{4} permits resolution of the molecular dynamics of the ammonium ions and leads to the conclusion that these ions are restricted rotators, prevented from freely rotating by comparatively low‐energy barriers.

Dynamic Mechanical Properties of Polystyrene Solutions from 23 to 300 MHz
View Description Hide DescriptionMeasurements of dynamic shear impedance at five frequencies from 23 to 300 MHz and at 25°C are reported for a monodisperse polystyrene as a function of concentration. The concentrations ranged from 3% to 20% polymer in di‐n‐butyl phthalate, a near‐theta solvent, and covered the region from the start of coil overlap to well beyond entanglement. Results are reported in terms of the in‐phase, , and quadrature, , components of the dynamic shear modulus of the polymer, where is the solvent contribution to the in‐phase modulus, is the angular frequency, is the dynamic solventviscosity, and is the volume fraction of solvent. The use of dynamic values for the solvent follows from observation of relaxation and non‐Newtonian behavior in the solvent beyond 100 MHz. The usual reduced variables method, even in this modified form, could not be successfully applied to superimpose data at different concentrations, indicating the need for further modification to account for finite concentration effects. The dynamic solution viscosity is found to increase with increasing concentration at fixed frequency. At any one concentration, it decreases with increasing frequency above 200 MHz. This is in contrast to the nearly constant values attained at lower frequencies at concentrations to 15% polymer; the decrease is too large to be accounted for by only solventviscosity effects. Results are also reported in terms of the reduced dynamic viscosity, where and are the steady‐flow values for the solution and the solvent, respectively. A high‐frequency limiting value of the reduced viscosity is found to obtain for the lower concentrations at the three lowest frequencies. However, for the highest concentration the limiting value is believed to occur at frequencies lower than those measured, so that a further decrease is, in fact, being observed above 100 MHz. An estimate of 10^{−1.04} was obtained for the reduced high‐frequency limiting viscosity in the limit of infinite dilution. From an estimate of the number of statistical segments (259) based on intrinsic viscosity measurements and on the results of Thurston, and an estimate of the extent of hydrodynamic interaction per segment, , of 0.2, a value of 1.9_{7} was obtained for , the ratio of the internal to segmental friction coefficients. The concentration dependence of was determined assuming little or no change in with concentration, and an appropriate dependence of on concentration and viscosity. It ranged from below entanglement to above it, approximately the one‐fourth and zeroth powers, respectively. The concentration dependence of increased by about while that of increased by on going from concentrations below to those above entanglement. Plots of the dynamic impedance against frequency indicate that departure from Newtonian behavior occurs sooner for the quadrature component than for the in‐phase part. Solvent relaxation was evaluated in terms of Lamb's semiempirical theory for low‐molecular‐weight liquids. From a comparison of the observed frequency dependence and the reference plots of Lamb, values for and , the high‐frequency limiting dynamic shear modulus and the average relaxation time, were obtained of 1.9_{7}×10^{10} dyn/cm^{2} and 8.5×10^{−12} sec, respectively. The magnitude of the latter is discussed and is shown to be in reasonable agreement with estimates of Pinnow, Candau, and Litovitz for n‐alkyl bromides. Based on values of the reduced dynamic viscosity obtained by Ferry, Holmes, Lamb, and Matheson at 73 kHz and upon the present results, it appears that the high‐frequency limiting viscosity of polystyrene in a near‐theta solvent persists for about decades before it decreases further at a frequency in the vicinity of that for the onset of solvent relaxation. Extension of optical techniques (e.g., Brillouin scattering) to studies of polymer solutions is briefly noted.

Infrared Spectrum of the Difluoromethyl Radical in Solid Argon
View Description Hide DescriptionWhen HCBrF_{2} and DCBrF_{2} at high dilution in argon are codeposited with an atomic beam of lithium on a CsI window at 15°K, lithium bromide absorptions appear along with several new absorptions not present when the precursor was deposited without alkali metal. These new absorptions are assigned to the antisymmetric hydrogen bending and carbon–fluorine stretching modes and the symmetric C–F vibration of the HCF_{2} and DCF_{2} radicals. The antisymmetric vibrational assignments are supported by product rule and normal coordinate calculations which give the potential constants , , and . An approximate force constant is calculated from the symmetric C–F vibration. The carbon–fluorine valence force constant for HCF_{2} is in the range of those for typical fluorocarbons.

Natural Orbital Expansion of Interacting Geminals
View Description Hide DescriptionAn antisymmetrized product of “interacting” geminals is proposed for the form of a many‐electron wavefunction. The interacting geminals are given a natural orbital expansion where the natural orbitals of the geminals are also natural orbitals of the total wavefunction. This ansatz is more general than the strongly and weakly orthogonal geminal and identical geminal models and includes them as particular cases. However, the use of the interacting geminal wavefunction is not significantly more complicated for the purpose of calculations. Different constraints on the geminal occupation coefficients define the various geminal models and more than one model can be incorporated into a single wavefunction. The case of two singlet pairs of electrons is examined in terms of the interacting geminal model—density matrices, energy expressions, and variational equations being given.

Dipole Davydov Splittings in Crystalline Anthracene, Tetracene, Naphthalene, and Phenanthrene
View Description Hide DescriptionThe contribution of dipole–dipole interactions to the Davydov splitting (i.e., the dipole Davydov splitting) of the moderately intense transitions of anthracene, tetracene, naphthalene, and phenanthrene has been investigated. Unlike most previous calculations, the Bose character of molecular excitons has been taken fully into account by using the classical theory of exciton states. In the dipole approximation this treatment is equivalent to the second quantized formulation of Agranovitch. Formulas are also derived for coupling of Born–Oppenheimer separable states through the full interaction potential. Dipole sums are calculated for infinite crystals by Ewald's method. High‐energy transitions are shown to make sizeable contributions to the Davydov splittings and are responsible for increasing polarization ratios of the 0–0 transition. For anthracene these high‐energy states push the splittings of the 3800‐Å system beyond the accepted values, implying that the residual intermolecular interactions due to higher multipole and exchange effects act in the opposite direction, thereby reducing the total splitting. In tetracene the dipole splittings, after including higher states, are in excellent agreement with experiment, thereby relegating multipoles, etc., to a minor role. The states of naphthalene and phenanthrene are subject to a pinching effect, due to the proximity of levels above and below, which inhibits the development of a large dipole splitting.

High‐Order ESR Transitions of Eu^{2+} in CaF_{2}, SrF_{2}, and BaF_{2}
View Description Hide DescriptionThe X‐band ESRspectra obtained from single crystals of CaF_{2}, SrF_{2}, and BaF_{2} containing dilute concentrations of Eu^{2+} ions show many weak absorption lines at magnetic field values lower than those of the allowed Eu^{2+} lines. These additional weak lines display a marked angular variation, but for a given crystal orientation, their relative field positions and ESR intensities are qualitatively similar for the three crystals. Calculations were made to determine the exact energy levels and probabilities of all high‐order ESR transitions for various crystal orientations as a function of the magnetic field strength. These calculations were based on the diagonalization of the energy matrix for the state in a cubic environment without use of the high‐field approximation. The observed field positions and relative ESR intensities of the additional low‐field lines were found to be qualitatively consistent with those calculated for the high‐order ESR transitions corresponding to of Eu^{2+} ions in cubic sites of the crystals.

Reactions of 2.8‐eV Tritium Atoms with Methane
View Description Hide DescriptionTritium atoms with 2.8‐eV kinetic energy have been formed by 1849‐Å photolysis of TBr, and have been reacted with CH_{4} in the presence of Br_{2}. In addition to HT from the abstraction reaction known in thermal systems, the direct substitution of T for H to form CH_{3}T has been observed. The ratio of HT/CH_{3}T is 3.6 to 4.0 in low Br_{2} mole fraction. In Br_{2} mole fractions exceeding 0.5, this ratio is reduced to 3.0, and the absolute yields of both HT and CH_{3}T are greatly reduced. The formation of HT and CH_{3}T from hot reactions of T with CH_{4} competes with the hot reaction of T with BR_{2} to form TBr.

Local Permutational Symmetry and the Separated‐Atom Limit
View Description Hide DescriptionLocal permutational symmetries are shown to supply approximate quantum numbers for a system composed of approximately localized subsystems. Local permutational symmetries associated with simple valence‐bond wavefunctions in the separated‐atom limit are studied and in certain cases are found to yield a nonphysical combination of local permutational symmetries. This nonphysical behavior can be avoided by use of a certain suitable form of configuration interaction or by a projection with either an appropriate chemically canonical matric basis element or a generalized structure projector.

Interaction of Two Metastable Triplet Helium Atoms
View Description Hide DescriptionAb initio quantum‐mechanical calculations have been performed for the , , and states arising from the interaction of two helium atoms. A rigorous upper bound to the quintet potential was found by use of the variational principle. Crude estimates of the autoionizing singlet and triplet states were obtained by the “stabilization” method. The quintet‐state potentials exhibit a van der Waals minimum, and the triplet and singlet potentials exhibit more substantial minima. The behavior of the wavefunctions in the separated‐atom limit was studied, and the range of applicability of the effective Heisenberg spin Hamiltonian was tested on the calculated potentials.

Excitation Energy of Tb^{3+} in Solids
View Description Hide DescriptionExcitation spectra of the emission of Tb^{3+} were measured in Sc(or In) BO_{3}, and Y (or Gd) BO_{3}, Y_{3}Ga_{5}O_{12}, Sc (or Y) PO_{4}, and Sc_{2} (or Y_{2}) O_{3} at room temperature. The excitation band is discriminated from the host lattice excitation band by inspecting the concentration dependences of the excitation spectra. The energy and the shape of the excitation band are almost the same in the lattices with the same structure. The band splittings are related to the symmetry of the crystalline field acting on Tb^{3+}. The excitation band is extremely enhanced by lowering temperature to 77°K.

Resonance Theory of Termolecular Recombination Kinetics: H+H+M→H_{2}M
View Description Hide DescriptionA theory is formulated for atomic recombination reactions which is based upon the identification of the set of transition complexes, , as specific quasibound states or orbiting resonances. The conventional “energy‐transfer mechanism” is assumed, since it has been justified under many experimental situations. Calculations, based on a modified distorted‐wave approximation, demonstrate that the main contribution to the rate is that arising from rotational (rather than vibrational) transitions downwards from the quasibound to the bound states. Computations were carried out for the reaction H+H+M→H_{2}+M for M = He, H_{2}, and Ar making use of detailed ab initio knowledge of the spectrum of quasibound states and their wave‐functions. Good agreement was found between the experimental rate constant and that calculated by the present resonance theory. The theory predicts a maximum in the rate in the temperature range between 65° and 100°K, attributed mainly to one particular quasibound state: . This suggests a promising region for further experimental investigation which could provide a critical check of the present theory.

Absolute Far‐Infrared Absorption Intensities of α‐Nitrogen
View Description Hide DescriptionThe absolute intensities of the translational lattice mode absorptions of α‐N_{2} in the far infrared have been measured. The experimental values are smaller by a factor of 5 than the calculated intensities obtained from a quadrupole‐induced mechanism theory. This discrepancy is discussed in terms of the model on which the theory was based. The intensity of the 50‐cm^{−1} line was found to be temperature dependent and decreased gradually between 15°K and 35°K. No discrete absorption was observed for the phase above 36°K. The 50‐cm^{−1} line has a width smaller than 0.5 cm^{−1} and the 70‐cm^{−1} line has a width of 6 cm^{−1}. Evidence was found for a decrease of the frequency of the 50‐cm^{−1} line as the phase transition temperature is approached.

Natural Orbitals, Divergences, and Variational Principles
View Description Hide DescriptionBogoliubov's principle of compensation of dangerous diagrams (PCDD) is extended to finite fermion systems and is shown to give Löwdin's natural spin–orbitals (NSO) which diagonalize the single‐particle reduced density matrix. Hartree–Fock theory corresponds to the compensation of the lowest‐order dangerous diagrams, which cause divergences in the perturbation expansion of the ground‐state energy. The PCDD is then derived from a variational principle that the number of particle–hole excitations in the true ground state is a minimum. The sense in which the NSO give the most rapid rate of convergence of the configuration‐interaction expansion of the true wavefunction is also discussed.

Rydberg States of Benzene in Rare‐Gas Matrices
View Description Hide DescriptionIn this paper we present experimental evidence for the observation of Rydberg states of benzene in solid Ar, Kr, and Xe. On the basis of semiquantitative theoretical evidence we argue that molecular Rydberg‐type states of a guest molecule are amenable to experimental observation in rare‐gas solids. These host matrices are characterized by a free electronlike conduction band, leading to a manifold of Wannier‐type states. The electron–atom interaction in rare‐gas solids is relatively weak so that the line broadening of these Rydberg‐type states will not be excessive. The identification of these “Rydberg‐type” states in a rare‐gas solid is based on matrix shifts, vibrational structure, isotope effects,linewidths, and site splittings. Two Rydberg‐type transitions of the benzene molecule were identified. From our analysis we conclude that: (a) The lowest molecular Rydberg state in the rare‐gas matrix can be correlated with the lowest Rydberg state in the gas phase, but is appreciably blue‐shifted. The blue shifts are: 6000 cm^{−1} for Ar, 3150 cm^{−1} for Kr, and 1610 cm^{−1} for Xe. (b) The benzene Rydberg levels in the rare‐gas matrix reveal some evidence for Jahn–Teller coupling effects, as is evident from the appearance of a nontotally symmetric vibrational component. (c) The linewidths observed for the Rydberg levels in the rare‐gas matrix are qualitatively consistent with theory. (d) The second Rydberg transition in the rare‐gas matrix is tentatively identified as corresponding to a Wannier state, which has no relation to the molecular levels of the isolated molecule. This assignment makes possible an estimate of the ionization potential of the molecule in rare‐gas solids. (e) Our results provide evidence that the lowest molecular Rydberg state and molecular impurity Wannier states are amenable to experimental observation in rare‐gas solids.

Optical Properties of Polymers: Model Calculations for Dinucleoside Phosphates
View Description Hide DescriptionThe optical properties(absorption,polarizability, circular dichroism, and optical rotatory dispersion) are calculated for models of dinucleoside phosphates using the time‐dependent Hartree theory with a simple free‐electron monomer model. Detailed results over the entire frequency spectrum have been obtained for a variety of dimer and polymer structures. The relation between the following conformational effects and the resulting polymeroptical properties were determined: base stacking and unstacking, helical winding and unwinding, and changes in distance between monomer planes. In addition, several other optical effects were calculated: the relative contributions of nearest and nonnearest neighbors along an infinite helical polymer; the effect of band half‐width on the observable splitting; and the relation between monomer and polymer line shape. The calculated results predict reasonable quantitative values as well as the main qualitative features of the experimental dinucleoside phosphate and polyribonucleotide spectra. The stacking–unstacking calculations are consistent with the experimental temperature dependencies of the hypochromism and optical rotation of ApA, and the right‐handed‐stacked conformation of this dimer is confirmed.

Configuration Interaction in the Simple Valence‐Bond Wavefunction for the Potential‐Energy Surfaces of Sigma‐Bonded Four‐Center Exchange‐Reaction Complexes
View Description Hide DescriptionThe two closed‐shell and nine open‐shell symmetry‐adapted MO electron configurations contained in the simple nonionic VB wavefunction for H_{4} in the limit of 2H_{2} with symmetry and in a complex are identified and their coefficients are obtained in terms of overlap integrals. Numerical comparison of the configuration coefficients obtained from the nonionic VB wavefunction with those obtained by the full CI calculation of Wilson and Goddard show that the ionic contribution to the complex of side is small in the ground state but significant in the upper state. The implications of a VB or CI treatment of four‐center potential‐energy surfaces regarding a recent extension of the Woodward–Hoffmann rules (conservation of orbital symmetry) to the reactions H_{2} + D_{2}→2HD and H_{2} + I_{2}→2HI are discussed.

Determination of Electrolyte Apparent Molal Compressibilities at Infinite Dilution Using a High‐Precision Ultrasonic Velocimeter
View Description Hide DescriptionUsing a newly designed high‐stability sing‐around circuit ultrasonic velocities in aqueous salt solutions down to concentrations of 2 × 10^{−4}mole/liter have been measured. Adiabatic apparent molal compressibilities at infinite dilution, and where possible standard molal compressibilities, have been determined for some aqueous solutions of tetra‐alkylammonium bromides, alkali‐metal chlorides and sulfates, and MgSO_{4}. The determination of these quantities from precise sound velocity, volumetric, and calorimetric measurements is discussed. The practice of obtaining from empirical extrapolation of data is shown to be unreliable and unnecessary.